<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-03-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001493594</issuerCik>
        <issuerName>MACOM Technology Solutions Holdings, Inc.</issuerName>
        <issuerTradingSymbol>MTSI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001239366</rptOwnerCik>
            <rptOwnerName>CHUNG PETER Y</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O SUMMIT PARTNERS</rptOwnerStreet1>
            <rptOwnerStreet2>222 BERKELEY STREET, 18TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5414</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>38407</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Remarks.</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents restricted stock units granted to Mr. Chung as part of the director compensation program. The restricted stock units will vest on February 15, 2021, and will settle solely by delivery of an equal number of shares of Common Stock provided that Mr. Chung remains in continuous service with the Issuer through the vesting date.</footnote>
        <footnote id="F2">Mr. Chung holds any restricted stock units for the benefit of Summit Partners, L.P. which he has empowered to determine when the underlying shares will be sold and which is entitled to the proceeds of any such sales. Summit Partners, L.P., through a two-person Investment Committee, responsible for voting and investment decisions with respect to the Issuer, currently composed of Martin J. Mannion and Peter Y. Chung, has voting and dispositive authority over the shares and restricted stock units reported herein and therefore may be deemed to beneficially own such shares. Summit Partners, L.P., Mr. Mannion and Mr. Chung disclaims beneficial ownership of the shares of common stock and the restricted stock units, except to the extent of their pecuniary interest therein.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>Robin W. Devereux, POA for Peter Y. Chung</signatureName>
        <signatureDate>2020-03-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
